Ms Siddiqi resigned on Monday, according to the company's publicity firm.

Mr Blunkett broke ministerial rules by taking the directorship without consulting an independent committee which advises former ministers on whether they should take up jobs.

Earlier, Tariq Siddiqi told BBC News he did not understand what all the "fuss" was about,

"With hindsight. it looks like there is a conflict of interest but if an MP does his job properly then he should be able to keep things apart," he said.

But in a statement, DNA Biotech said: "Lucy Siddiqi has resigned as a director of the company due to the considerable pressure brought upon Lucy and her family under the current intense media attention."